[EM] Re: How to describe RAV/ARC

[Ted Stern]

Hi Forest,

Apparently I missed your interactions with Bart on this list, but I'll take
your word for it. ;-)

On 15 Mar 2005 at 14:12 PST, Forest Simmons wrote:
> But now let me continue on to a sales pitch for a related method:
>
> We got the set P by eliminating all of the candidates that both Approval 
> and Condorcet agree should be eliminated.
>
> The remaining candidates are the subjects of irreconcilable disagreement:
>
> As we noted above, they are totally ordered by by the ordinary pairwise 
> beat relation, but I forgot to mention that they are also totally ordered 
> by approval order.
>
> That would be fine except that these two orders are diametrically opposed; 
> one is the exact reverse of the other.

No, not exactly, but I won't quibble.

>
> In other words the set P is the set of candidates on which approval and 
> Condorcet have irreconcilable disagreement.

But approval doesn't rank candidates.  Approval is yes/no.

The approval winner has highest approval, but you don't know whether the
approval winner was 1st, 2nd or 3rd on most of the ballots.

So highest approval gives you a good measure of average upper rank, but not
whether one candidate is better than another.

Condorcet gives you relative ranking without upper lower rank.

So each has something to contribute, which is why I like Approval-seeded
Bubble Sort.  Approval-seeding gives higher-ranked candidates an edge, but
Condorcet tells you how they match up against each other.

>
> Any unbiased compromise between Approval and Condorcet must give each 
> member of P a chance of winning.

As I said before, I don't agree that an unbiased compromise is desirable.

>
> Random ballot from P results in a fair chance that is monotonic and clone 
> proof.

Well, I'm with you part way, up to the 'unbiased compromise' part.  I'm
dubious that anybody would agree to a random ballot idea, but I guess I
wouldn't oppose it if the electorate thinks it's the most acceptable idea.

By the way, I attempted to describe some of these ideas to a colleague, who
has a Ph.D. in math.  I was surprised at how hard it was to explain some of
the concepts, and he is a very quick study.  I realized that it is easy to
describe Approval, moderately easy to explain ranked ballots, but nearly
impossible to describe and motivate why one would want to rank candidates
below the approval cutoff.  Especially if unranked candidates are disapproved.

One thought I had is that there are actually 3 categories of candidates.

Preferred      Not preferred, but not rejected      Outright rejected
                 (Hold your nose and swallow)

"Approval cutoff" is actually the line between Preferred and Not Rejected,
with unranked candidates going into the Outright-rejected group.

When you look at it that way, Approval ratings below 50 percent are not so
terrible.

That's almost an argument for Cardinal Ratings seeding instead of Approval
seeding, isn't it?

Ted
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